What is your recommendation for an in-depth introductory combinatoric book? A book that doesn’t just tell you about the multiplication principle, but rather shows the whole logic behind the questions with full proofs. The book should be for a first-year-student in college. Do you know a good book on the subject?

Thanks.

**Answer**

My personal favorites are the following:

- Introduction to Combinatorial analysis [Riordan]
- Concrete Mathematics [Graham, Knuth, Patashnik]
- Enumerative Combinatorics vol. 1 [Richard Stanley]

(is not always that introductory, but for those who like counting, it is a must have)

If you want really easy, but still interesting books, you might like Brualdi’s book (though apparently, that book has many mistakes). Also interesting might be some chapters from Feller’s book on Probability (volume 1).

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